Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20287849 | C2 | semidirect |
| 2. C2×#16811059 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20276431 | C2 | semidirect |
| 5. #20275613 | C2 | semidirect |
| 6. #20272801 | C2 | semidirect |
| 7. C53×#3155 | C2 | semidirect |
| 38. C2×Dic212 | D4 | semidirect |
| 40. C2×D424 | D4 | semidirect |
| 51. #13133157 | D4 | semidirect |
| 53. C2×#11719908 | D4 | semidirect |
| 213. #3155 | D53 | semidirect |
| 250. C53 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| C2×#16811059 | 2 |
| #20276451 | 2 |
| #20276431 | 2 |
| #20275613 | 2 |
| #20272801 | 2 |
| C53×#3155 | 2 |
| #13334 | 53 |